The receptive fields of visual neurons are known to be retinotopically arranged, and in awake animals they "move" with gaze, maintaining the same retinotopic location regardless of eye position. Here, we report the existence in the monkey parietal cortex of cells (called "real-position" cells) whose receptive field does not systematically move with gaze. These cells respond to the visual stimulation of the same spatial location regardless of eye position and therefore directly encode visual space in craniotopic instead of retinotopic coordinates.